please answer all 3 questions

Answer:

Question 6 :  True

Question 7:  False

Step-by-step explanation:

To find g(f(x)) given f(x) and g(x), substitute the expression for f(x) for every x in g(x)

f(x) = 2x

g(x) = x²

g(f(x) = (2x)² = 4x²

So True

f(x) = x² + x

g(x) = 2x + 1

g(f(x)) = 2(x² + x) + 1 = 2x² + 2x + 1

So False

Using z - score, the percentage of students above 83 is 15.9%

To find the number of students that scored above 83 can be calculated using z - score formula.

This is given as

z = x - μ / σ

Substituting the values into the formula;

z = 83 - 75 / 8

z = 1

The z-score is 1

Let's find the percentage of z -score under the score

p(x > 83) = 1 - P(x < 83) = 0.15866

p = 15.9%

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The type of model that best fits the situation of a $500 raise in salary each year is a linear model.

In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.

In the given case, the dependent variable is the salary and the independent variable is the year.

You may build a table to show that for increments of 1 year the increments of the salary is $500:

Year         Salary        Change in year         Change in salary

2010           A                           -                                       -

2011           A + 500     2011 - 2010 = 1          A + 500 - 500 = 500

2012          A + 1,000   2012 - 2011 = 1          A + 1,000 - (A + 500) = 500

So, you can see that every year the salary increases the same amount ($500).

In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).              

In this case, m = $500 and b is the starting salary: y = 500x + b.

The value of Sin A is 5/13.

Option A is the correct answer.

We have,

Sin A = Perpendicular / Hypotenuse

Sin A = BC / AB

And,

BC = 5

AB = 13

Substituting.

Sin A = 5/13

Thus,

The value of Sin A is 5/13.

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Answer:

the percentage of red marbles in the bag is 30%.

Step-by-step explanation:

To find the percentage of red marbles in the bag, we need to divide the number of red marbles by the total number of marbles and then multiply by 100:

Percentage of red marbles = (Number of red marbles / Total number of marbles) x 100

Number of red marbles = 12

Total number of marbles = 40

Percentage of red marbles = (12/40) x 100

= 0.3 x 100

= 30%

Therefore, the percentage of red marbles in the bag is 30%.

Answer:

just start scamming

Step-by-step explanation:

The distance of the perpendicular from Q to line PR is D = 2.2135 units

Given data ,

Let the triangle be represented as ΔPQR

Now , the coordinates are P(1, 3), Q(5, 4) and R(5, 15)

And , the equation of line of PR is given by

Slope m = ( 15 - 3 ) / ( 5 - 1 )

m = 3

y - 3 = 3 ( x - 1 )

Adding 3 on both sides , we get

y = 3x

y - 3x = 0

And , the point is Q(5, 4)

Now , distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )

D = | ( 1 ) ( 5 ) + ( -3 ) ( 4 ) + 0 | / √ ( 1 )² + ( 3 )²

D = | 5 - 12 | / √10

D = 7/√10

D = 2.2135 units

Hence , the distance is 2.2135 units

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The question that Diondra would ask that does not allow for variability is A. Which movie did her best friend like the most?

The other three questions ("How many awards did each movie win?", "What is the total dollar amount that each movie made from ticket sales?", and "How many weeks did each movie play in the theater?") all offer metrics by which a movie's popularity could be measured, and those measurements could vary from movie to movie.

However, the question about her best friend's favorite movie depends solely on the opinion of one individual, not a variable measure, and therefore doesn't allow for variability.

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The volume of water that the pool can hold is  150.72 cubic centimeters.

Remember that the volume of a cylinder of radius R and height H is:

V = pi*R²*H

Where pi = 3.14

For the pool we know that the height is H = 3ft, and the diameter is 8ft, then the radius is R = 8ft/2 = 4ft

Replacing that in the volume formula we will get:

V = 3.14*(4cm)²*3cm

V = 150.72 cubic centimeters.

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The exponential function that model this situation is [tex]A(t) = 2500(1 + 0.035)^t.[/tex]

The account will have $5000 in 20 years.

Let A be the amount in the account after t years.

Then, we can model this situation with the function A(t) = 2500(1 + 0.035)^t with the use of compound intererst formula which is [tex]P = A*(1+r)^t[/tex]

To find when the account will have $5000, we can set A(t) = 5000 and solve:

5000 = 2500(1 + 0.035)^t

2 = (1.035)^t

Taking the natural logarithm:

ln(2) = t ln(1.035)

t = ln(2)/ln(1.035)

t = 20.148791684

t = 20 years.

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Answer:

1)  21 years

2) 26 years

Step-by-step explanation:

To model the account balance of Vanessa's account at t years, we can use an exponential function in the form:

[tex]\large\boxed{A(t) = A_0(1 + r)^t}[/tex]

where:

Given Vanessa invested $2500 into the account and it will increase in value by 3.5% each year:

Substitute these values into the formula to create an equation for A in terms of t:

[tex]A(t) = 2500(1 + 0.035)^t[/tex]

[tex]A(t) = 2500(1.035)^t[/tex]

To find when the account balance will be $5000, set A(t) equal to $5000 and solve for t:

[tex]A(t)=5000[/tex]

[tex]2500(1.035)^t=5000[/tex]

[tex](1.035)^t=\dfrac{5000}{2500}[/tex]

[tex](1.035)^t=2[/tex]

[tex]\ln (1.035)^t=\ln 2[/tex]

[tex]t \ln 1.035=\ln 2[/tex]

[tex]t=\dfrac{\ln 2}{ \ln 1.035}[/tex]

[tex]t=20.1487916...[/tex]

[tex]t=20.15\; \sf years\;(2\;d.p.)[/tex]

Therefore, it will take approximately 20.15 years for Vanessa's account to reach a value of $5000.

Since the interest rate is an annual rate of 3.5%, it means that the interest is applied once per year, at the end of the year. Therefore, we need to round up the number of years to the next whole number.

So Vanessa's account will have $5,000 after 21 years.

Note: After 20 years, the account balance will be $4,974.47. After 21 years, the account balance will be $5,148.58.

[tex]\hrulefill[/tex]

To model the increase in movie ticket prices over time, we can use an exponential function in the form:

[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]

where:

Given the initial price of the ticket was $4.22 and the price has increased by 3.1% each year:

Substitute these values into the formula to create an equation for P in terms of t:

[tex]P(t) = 4.22(1 + 0.031)^t[/tex]

[tex]P(t) = 4.22(1.031)^t[/tex]

To find how many years until tickets cost $9.33, we can set P(t) equal to $9.33 and solve for t:

[tex]P(t)=9.33[/tex]

[tex]4.22(1.031)^t=9.33[/tex]

[tex](1.031)^t=\dfrac{9.33}{4.22}[/tex]

[tex]\ln (1.031)^t=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]

[tex]t \ln (1.031)=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]

[tex]t =\dfrac{\ln \left(\dfrac{9.33}{4.22}\right)}{\ln (1.031)}[/tex]

[tex]t=25.9882262...[/tex]

Therefore, it will take approximately 26 years for movie ticket prices to reach $9.33, assuming the annual growth rate remains constant at 3.1%.

The value of number of students who failed in both mathematics and English is 40.

Since, Given that;

60% of the 1000 students passed the examination,

Hence, we can calculate the number of students who passed the exam as follows:

60/100 x 1000 = 600

So, 600 students passed the examination.

Now, let's find the number of students who failed the examination.

Since 60% of the students passed, the remaining 40% must have failed. Therefore, the number of students who failed the examination is:

40/100 x 1000 = 400

Of the 400 failing students, we know that 60% failed in mathematics.

So, the number of students who failed in mathematics is:

60/100 x 400 = 240

Similarly, we know that 50% of the failing students failed in English.

So, the number of students who failed in English is:

50/100 x 400 = 200

Now, we need to find the number of students who failed in both subjects.

We can use the formula:

Total = A + B - Both

Where A is the number of students who failed in mathematics, B is the number of students who failed in English, and Both is the number of students who failed in both subjects.

Substituting the values we have, we get:

400 = 240 + 200 - Both

Solving for Both, we get:

Both = 240 + 200 - 400

Both = 40

Therefore, the number of students who failed in both mathematics and English is 40.

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a) The area of the entire trapezoidal rear window =  882 sq.in.

b) The fractional part of a complete circle is cleared on the rear window by the 18-inch wiper = 5/12

c) The area of the part of the rear window that is cleared by the wiper = 424.12 sq. in.

d) The percent of the area of the entire rear window is cleared by the wiper =  48.09%

We know that the formula for the area of trapezoid,

A = ((a + b) / 2) × h

Here, a = 36 in., b = 48 in. and height of the trapezoid h=21 in

Using above formula, the area of the entire trapezoidal rear window would be,

A = ((36 + 48) / 2) × 21

A = 882 sq.in.

Here, the 18-inch rear window wiper clears a 150° sector of a circle on the rear window.

We know that the measure of entire circle = 360°

So, the fractional part of a complete circle is cleared on the rear window by the 18-inch wiper would be,

150° / 360° = 5/12

Now we need to find the area of the part of the rear window that is cleared by the wiper.

We know that the formula for the area of sector of a circle is:

A = (θ/360) × πr²

Here, the central angle θ = 150° and radius r = 18 in.

A = (θ/360) × πr²

A = (150/360) × π × 18²

A = 424.12 sq. in.

Now we need to find the percent of the area of the entire rear window is cleared by the wiper.

P = [(area of the part of the rear window cleared by the wiper) / (area of the entire trapezoidal rear window)] × 100

P = (424.12 / 882) × 100

P = 48.09%

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The number 1.3 is both a rational and an irrational number.

The number 1.3 is a rational number because it can be expressed as the quotient of two integers, namely 13/10.

The number 1.3 an irrational number because it cannot be expressed as the ratio of two integers, without repeating or terminating decimals, and its decimal representation goes on forever without repeating.

So we can conclude that the number 1.3 is both rational and irrational number.

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The critical values t₀ for a two-sample t-test is ± 2.0.6

To find the critical values t₀ for a two-sample t-test to test the claim that the population means are equal (i.e., µ₁ = µ₂), we need to use the following formula:

t₀ = ± t_(α/2, df)

where t_(α/2, df) is the critical t-value with α/2 area in the right tail and df degrees of freedom.

The degrees of freedom are calculated as:

df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]

n₁ = 14, n₂ = 12, X₁ = 6,X₂ = 7, s₁ = 2.5 and s₂ = 2.8

α = 0.05 (two-tailed)

First, we need to calculate the degrees of freedom:

df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]

= (2.5²/14 + 2.8²/12)² / [(2.5²/14)²/13 + (2.8²/12)²/11]

= 24.27

Since this is a two-tailed test with α = 0.05, we need to find the t-value with an area of 0.025 in each tail and df = 24.27.

From a t-distribution table, we find:

t_(0.025, 24.27) = 2.0639 (rounded to four decimal places)

Finally, we can calculate the critical values t₀:

t₀ = ± t_(α/2, df) = ± 2.0639

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a) The fourth and sixth data points have significantly different ratios.

a) Let's calculate the ratios:

For the first data point:

= 11.5 gallons / $25.23 = 0.4555 gallons per dollar

For the second data point:

= 7.2 gallons / $15.80 = 0.4557 gallons per dollar

For the third data point:

= 10 gallons / $21.94 = 0.4556 gallons per dollar

For the fourth data point:

= 14.3 gallons / $40.63 = 0.3519 gallons per dollar

For the fifth data point:

= 6.8 gallons / $14.92 = 0.4555 gallons per dollar

For the sixth data point:

= 9.7 gallons / $27.56 = 0.3517 gallons per dollar

However, the fourth and sixth data points have significantly different ratios.

b) If the relationship is not proportional, the data values that should be changed to make the relationship proportional are the fourth and sixth data points.

The difference in ratios could be explained by factors such as fluctuations in gas prices or differences in gas grades.

To establish a proportional relationship, it would be necessary to collect data where the price per gallon remains constant for all data points or to separate the data based on gas grades and analyze each grade separately.

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Answer:

In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio (r).

In this case, the first term (a₁) is 2, and the common ratio (r) can be found by dividing any term by its preceding term. Let's calculate it:

r = 6 / 2 = 3

Now, to find the 15th term (a₅₊₁₋₅), we can use the formula:

aₙ = a₁ * r^(n-1)

Substituting the values, we have:

a₁ = 2

r = 3

n = 15

a₁₅ = 2 * 3^(15-1)

Calculating the exponent first:

3^(15-1) = 3^14 = 4782969

Now, substituting this value back into the formula:

a₁₅ = 2 * 4782969

a₁₅ = 9565938

Therefore, the 15th term of the geometric sequence 2, 6, 18, ... is 9565938.

Step-by-step explanation:

The calculated value of the unit rate of the situation is (c) $12 per hour

From the question, we have the following parameters that can be used in our computation:

$60.00 in 5 hours

This means that

Time = 5 hours

Total costs = $60.00

using the above as a guide, we have the following:

Unit rate = Total costs / time

substitute the known values in the above equation, so, we have the following representation

Unit rate = 60.00/5

Evaluate

Unit rate = 12

Hence, the unit rate of the situation is (c) $12 per hour

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The other information can the student use to establish the AA criterion is Angle LMN congruent angle LQR or angle LMN congruent angle LRQ

The student can use the following information to establish the AA criterion:

These two angles correspond to the two angles in the other triangle (LQR or LRQ) that are not congruent to the angle already known to be congruent (angle QLR).

Therefore, the AA congruent for similarity can be congruent .

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If a top travels 8 centimeters each time it is spun and it is spun 7 times, the total distance it travels is 56 centimeters.

The total distance is determined by multiplication of the distance traveled per spin and the number of spins.

Multiplication involves the multiplicand, the multiplier, and the product.

The traveling distance per spun = 8 centimeters

The number of spinning of the top = 7 times

The total distance = 56 centimeters (8 x 7)

Thus, using multiplication, the total distance the top travels after the 7th spin is 56 centimeters.

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The height of rectangular prism B is 5 yards.

Let's first find the volume of rectangular prism B:

The volume of the solid figure = Volume of prism A + Volume of prism B

180 = 75 + length × width × height of prism B

105 = length × width × height of prism B

We know that the length of prism B is 7 yards and the width is 3 yards,

Substitute those values:

105 = 7 × 3 × height of prism B

105 = 21 × height of prism B

height of prism B = 105/21

height of prism B = 5

Therefore, the height of rectangular prism B is 5 yards.

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You can write 27% as a fraction like this: [tex]\frac{27}{100}[/tex] . (27/100).

Or as a decimal 0.27.

The parabola y = x² scaled vertically by a factor of 1/10 gives y = x²/10

From the question, we have the following parameters that can be used in our computation:

The parabola y = x² is scaled vertically by a factor of 1/10

The rule of this transformation is

Image = (x, ay)

Where

a = 1/10

So, we have

y = 1/10 * x²

Evaluate

y = x²/10

Hence, the image of the function is y = x²/10

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Answer:

y- intercept = - 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = 2 , then

y = 2x + c ← is the partial equation

to find c substitute (5, 4 ) into the partial equation

4 = 2(5) + c = 10 + c ( subtract 10 from both sides )

- 6 = c

that is the y- intercept c = - 6

The total amount to each person end up paying $20.54.

To find the total amount each person will pay, first calculate the 20% tip on the total bill and then divide the sum by the number of people.

To split the bill evenly among Raphael and his four friends, we first need to find the total cost including the 20% tip.

The tip is 20% of the original bill, which is equivalent to 0.20 x $85.60 = $17.12.

Therefore, the total cost of the bill with the tip is $85.60 + $17.12 = $102.72.

To split this evenly among the five people, we divide by 5:

$102.72 ÷ 5 = $20.54

So each person will end up paying $20.54.

20% of $85.60 is ($85.60 * 0.20) = $17.12

Add the tip to the total bill:

$85.60 + $17.12 = $102.72

Divide the total amount by the number of people (5): $102.72 / 5 = $20.54

Therefore, the answer is B. $20.54.

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If the population in the year 2007 is 111.3 million, then the population in the year 2044 will be 148.37 million.

In order to find the population in the year 2044, we use the population growth formula; which is : P = P₀ × (1 + r)ⁿ;

where P = future population, P₀ = initial population, r = annual growth rate, and n = number of years;

Substituting the values,

We get;

⇒ P = (111.3 million) × (1 + 0.0078)²⁰⁴⁴⁻²⁰⁰⁷;

Simplifying this expression,

We get;

⇒ P = (111.3 million) × (1.0078)³⁷;

⇒ P ≈ 148.37 million;

Therefore, the population in the year 2044 is estimated to be approximately 148.37 million.

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Answer:

24 cakes.

Step-by-step explanation:

6 cups of oil divided by 1/4 cup oil per cake = 24 cakes

6/(1/4) = 24

or 6/(0.25) = 24

She can make 24 cakes with 6 cups of oil.

The number of lego planes that can be build in 40 minutes is A = 2.33

Given data ,

Johnny can build in 3 1/2 lego planes in 60 minutes

On dividing the number of planes he can build in 60 minutes (3 1/2) by 60:

From the proportion , we get

To find out how many planes he can build in 40 minutes, we can multiply the amount he can build in one minute by 40:

3.5 / 60 = A / 40

Multiply by 40 on both sides , we get

A = 2.33

Hence , Johnny can build approximately 2.33 lego planes in 40 minutes

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